Littlewood-Paley Theory for the Differential Operator partial derivative(2)/partial derivative x(1)(2) partial derivative(2)/partial derivative x(2)(2) - partial derivative(2)/partial derivative x(3)(2)

摘要

Littlewood-Paley theory for the differential operator, Delta D = partial derivative x(1)(2) partial derivative x(2)(2) - partial derivative x(3)(2), is developed. This study leads to the introduction of a new class of Triebel-Lizorkin spaces.F-p(alpha,q)(D) associated with the dilation (x(1), x(2), x(3)) --> (2(V1) x(1) 2(v2) x(2), 2(v1) +1'213), (V-1, V-2) is an element of Z(2). The corresponding atomic and molecular decompositions are obtained. A frame generated by modulations, dilations and translations is also studied. Using this result, we show that Delta D is a linear isomorphism front F-p(alpha,q)(D) to F-p(alpha-2-q)(B).